Unit of ionic mobility is :

Options

A. `mV^(-1)s^(-1)`
B. `m^(2)V^(-2)s^(-1)`
C. `m^(2)V^(-1)s^(-1)`
D. `m^(-2)Vs^(-1)`

Answer

To determine the unit of ionic mobility, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Ionic Mobility**: Ionic mobility (µ) is defined as the velocity (v) of an ion moving through a medium (like a gas or liquid) under the influence of an electric field (E).

2. **Identify the Relationship**: The relationship can be expressed as:
\[ \mu = \frac{v}{E} \]
where:
- \( \mu \) = ionic mobility
- \( v \) = velocity of the ion
- \( E \) = electric field strength

3. **Units of Velocity**: The unit of velocity (v) is distance per time. In SI units, this is:
\[ \text{Velocity (v)} = \text{meters per second} = \text{m/s} \]

4. **Units of Electric Field**: The unit of electric field (E) is defined as the potential gradient, which is:
\[ \text{Electric Field (E)} = \text{volts per meter} = \text{V/m} \]

5. **Substituting Units into the Formula**: Now we can substitute the units of velocity and electric field into the equation for ionic mobility:
\[ \mu = \frac{\text{m/s}}{\text{V/m}} \]

6. **Simplifying the Units**: When we divide the units, we can simplify it as follows:
\[ \mu = \frac{\text{m/s}}{\text{V/m}} = \frac{\text{m}}{\text{s}} \times \frac{\text{m}}{\text{V}} = \frac{\text{m}^2}{\text{s} \cdot \text{V}} \]

7. **Final Unit of Ionic Mobility**: Therefore, the unit of ionic mobility is:
\[ \mu = \frac{\text{m}^2}{\text{s} \cdot \text{V}} \]
This means the correct option for the unit of ionic mobility is \( \text{m}^2/\text{s} \cdot \text{V} \).

### Conclusion:
The unit of ionic mobility is \( \text{m}^2/\text{s} \cdot \text{V} \).

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